Proceedings of the Edinburgh Mathematical Society

Table of Contents - Volume 34 - 1915  

Research Article

Real Linear Substitutions with Equimodular Multipliers, and their expression in terms of their Invariants

Dr D. G. Taylor

§1. Let

S0013091500029540_eqn1

denote a linear substitution of non-vanishing determinant; and let the roots k∈ of its characteristic equation

S0013091500029540_eqn2

be for the present assumed distinct. Then with each root k∈ is associated an invariant point or pole P∈, and a linear invariant, or invariant (n−2)-plane ξ∈. If the n points P∈ do not lie on an (n−2)-plane, the determinant of their coordinates,

S0013091500029540_eqn3

(Received November 04 1916)

(Accepted December 10 1916)